CONGESTION REDUCTION OF LTE NETWORKS
Optimal reduction of 4G LTE cellular network congestion utilizes two components of learning and optimization. First, an MLPDL learning approach is used to model cellular network congestion measured in terms of PRB utilization and predict 80% utilization as breakpoint thresholds of cellular towers as a function of average connected user equipments. Then, an optimization problem is formulated to minimize LTE network congestion subject to constraints of user quality and load preservation. Two alternative solutions, namely Block Coordinated Descent Simulated Annealing (BCDSA) and Genetic Algorithms (GA) are presented to solve the problem. Performance measurements demonstrate that GA offers higher success rates in finding the optimal solution while BCDSA has much improved runtimes with reasonable success rates. Accordingly, integrated iterative methods, programs, and systems are described aiming at minimizing the congestion of 4G LTE cellular networks by redistributing traffic from congested cellular towers to noncongested cellular towers.
The present application is related to U.S. Provisional Patent Application Ser. No. 62/348,098, filed on Jun. 9, 2016 which is incorporated herein by reference and to which priority is claimed pursuant to 35 USC 119 and to application Ser. No. 15/488,330, filed on Apr. 14, 2017, which is incorporated herein by reference and to which priority is claimed pursuant to 35 USC 120.
FIELD OF THE INVENTIONThe present invention relates to methods, programs, and systems for reducing the overall congestion of a 4G Long Term Evolution (LTE) cellular networks by means of redistributing traffic from congested cellular towers to their noncongested neighboring cellular towers.
BACKGROUND OF THE INVENTIONDue to exponential growth of LTE traffic, mobile operators are spending hundreds of millions of dollars improving their cellular infrastructure. Different capacity improvement and congestion mitigation approaches include spending major capital to acquire new spectrum, building new macro sites to add bandwidth, and building small cells as well as inbuilding solutions. These approaches have proven effective in certain cases but are expensive and not always practical when facing challenges associated with dynamic capacity demands. When facing dynamic capacity demands and in the absence practically viable systematic optimization approaches, mobile operators exercise manual finetuning of cellular network parameters in order to alleviate cellular congestion. However, the results are trivially suboptimal compared to systematic optimization approaches. This invention presents systematic approaches to optimally reduce the congestion of LTE networks.
The capacity challenge in LTE networks is better understood by explaining how resources are allocated to users. Under LTE standard, each cellular tower has a fixed number of Physical Resource Blocks (PRBs) defined in time and frequency. Utilization of each PRB is independent of utilization of other PRBs within the same cell without causing interfere. When a user requests a certain type of service or Enhanced Radio Access Bearer (ERAB), the LTE scheduler at a cellsite will allocate a certain number of PRBs depending on the type of service, i.e., guaranteed bit rate versus nonguaranteed bit rate, required bandwidth, required latency, and most importantly the maximum throughput that can be carried. This throughput associated with each PRB mainly depends on the maximum allowable modulation scheme ranging from QPSK at the lowest level to 16QAM and up to 64QAM. The maximum allowable modulation depends on the Signal to Interference and Noise Ratio (SINR) experienced by a given user for that PRB. For example, a user requesting video streaming while experiencing excellent RF conditions and hence high SINRs will be able to use high modulation schemes such as 64QAM per each PRB assigned and will hence require a small number of PRBs to satisfy its requested ERAB. On the other hand, a user experiencing subpar RF conditions and hence poor SINRs will only be able to utilize low modulation schemes such as QPSK hence requiring a much larger number of PRBs than the previous user in order to satisfy a similar video streaming quality [8].
In order to mitigate the issue noted above, most operators attempt at keeping per cell PRB utilization under a congestion threshold of 80%. The reserved 20% capacity of the cell can then be used to service handover requests and provide a safety margin to avoid denial of handover requests. Cells exceeding the congestion threshold usually trigger augmentation mechanisms such as carrier additions or bandwidth expansions. In an effort to keep PRB utilization under the limit of 80%, it is critical to manage traffic amongst various cells where traffic from highly loaded cells is offloaded to lightly loaded cells serving the same area. This traffic offload can be achieved in several manners, i.e., by changing the footprint of cells, shifting cell boundaries, and changing tilts as well as azimuths of cells. However, implementing physical changes is time consuming and more suited for static or slowly changing environments as oppose to fast changing dynamic environments.
Alternatively, this invention introduces changing the power of a cell i referred to as _{i }and handover threshold of a cell i referred to as _{i }in order to control the serving area of said cell and redistribute traffic as needed. These parameters can be changed instantly in the field in response to dynamic changes in traffic distributions in order to offload traffic from congested cells to neighboring cells. Caution has to be exercised such that traffic offloading is done without congesting the neighboring cells and without degrading the quality of the UEs on the edge of congested cells that end up shifting to a neighboring cell.
The phrases cell, cell tower, and cellular tower are used interchangeably in the disclosure of this invention.
BRIEF SUMMARY OF THE INVENTIONThe subject disclosure features a method that effectively predicts the average number of connected UEs associated with PRB utilization congestion threshold of 4G LTE cellular towers and provides a dynamic automated solution that significantly reduces the congestion of LTE networks by redistributing traffic from congested cells to the noncongested cells automatically.
In an embodiment illustrated by
An embodiment of the present invention comprises a MultiLayer Perceptron Deep Learning (MLPDL) structure that can be iteratively trained by real network measurement data collected from 4G LTE cellular towers to accurately predict the average number of connected UEs associated with PRB utilization congestion threshold of cellular towers.
In a preferred embodiment illustrated by
In preferred embodiments, MLPDL technique can improve accuracy of predicting the average number of connected UEs associated with PRB utilization congestion threshold. In such embodiments, accuracy of prediction is calculated by root mean square error results where root mean square error decreases as the number of input measurements increases per cellular tower.
A further embodiment of the present invention comprises a detailed formulation of an optimization problem with the objective of minimizing the congestion of a collection of cellular towers beyond their predicted PRB utilization congestion threshold through traffic offloading and subject to constraints associated with preserving the overall cluster load as well as minimum quality thresholds experienced by connected user equipments.
Additional embodiments of the present invention feature solving this optimization problem using two algorithmic alternatives, namely, Block Coordinated Descent Simulated Annealing (BCDSA) and Genetic Algorithm (GA).
In one embodiment, adjusting power or handover threshold of individual cellular towers results in shifting cellular tower borders, redistributing traffic from congested cellular towers to noncongested cellular towers, and reducing congestion.
In one preferred embodiment, BCDSA algorithm described in Algorithm 2 provides an automatic iterative process to reduce congestion and optimally utilize the capacity of a 4G LTE cellular network by applying changes to two sets of decision variables, i.e., power and handover threshold of cellular towers. In such embodiment, BCDSA algorithm applies changes to one set of decision variables at a time while keeping the other set fixed at that time. Then, it alternates between the set of power and power margin decision variables based on freeze thresholds.
In another preferred embodiment, GA algorithm described in Algorithm 2 provides an automatic iterative process to reduce congestion and optimally utilize the capacity of a 4G LTE cellular network by applying changes to two sets of decision variables, i.e., power and handover threshold of cellular towers.
In an integrated embodiment illustrated by

 importing per cellular tower information (101) including neighbor handover, traffic demand, traffic carried, average transmit power, and minimum acceptable quality;
 waiting for the expiration of a refresh timer (102);
 importing collected learning measurements since the beginning till the last period (103) upon expiration of said refresh timer;
 applying an MLPDL (104) technique to predict breakpoints of the plurality of cellular towers one cellular tower at a time, wherein the breakpoint of a cell tower reflects the average number of users connected to said cell tower associated with the preferred maximum PRB utilization percentage of said cellular tower;
 applying the optimization inputs (105), i.e., imported topology information and predicted PRB utilization congestion thresholds;
 choosing the optimization algorithm (106);
 if BCDSA algorithm is chosen, performing BCDSA algorithm (107) to redistribute traffic as the result of changing power and handover thresholds of the plurality of cells to effectively redistribute traffic from a congested cells to noncongested cells thereby optimally reducing the congestion of the cellular network;
 if GA algorithm is chosen, performing GA algorithm (108) to redistribute traffic as the result of changing power and handover thresholds of the plurality of cells to effectively redistribute traffic from a congested cells to noncongested cells thereby optimally reducing the congestion of the cellular network;
 collecting the operating parameters of cellular towers from either BCDSA or GA algorithm (109); and
 going back to step (102) to wait again for the expiration of said refresh timer.
In another integrated embodiment illustrated by

 code for importing per cellular tower information (101) including neighbor handover, traffic demand, traffic carried, average transmit power, and minimum acceptable quality;
 code to wait for the expiration of a refresh timer (102);
 code for importing collected learning measurements since the beginning till the last period (103) upon expiration of said refresh timer;
 code for applying an MLPDL (104) technique to predict breakpoints of the plurality of cellular towers one cellular tower at a time, wherein the breakpoint of a cell tower reflects the average number of users connected to said cell tower associated with the preferred maximum PRB utilization percentage of said cellular tower;
 code for applying the optimization inputs (105), i.e., imported topology information and predicted PRB utilization congestion thresholds;
 code for choosing the optimization algorithm (106);
 if BCDSA algorithm is chosen, code for performing BCDSA algorithm (107) to redistribute traffic as the result of changing power and handover thresholds of the plurality of cells to effectively redistribute traffic from a congested cells to noncongested cells thereby optimally reducing the congestion of the cellular network;
 if GA algorithm is chosen, code for performing GA algorithm (108) to redistribute traffic as the result of changing power and handover thresholds of the plurality of cells to effectively redistribute traffic from a congested cells to noncongested cells thereby optimally reducing the congestion of the cellular network;
 code for collecting the operating parameters of cellular towers from either BCDSA or GA algorithm (109); and
 code for going back to step (102) to wait again for the expiration of said refresh timer.
In yet a further integrated embodiment illustrated by

 importing per cellular tower information (101) including neighbor handover, traffic demand, traffic carried, average transmit power, and minimum acceptable quality;
 waiting for the expiration of a refresh timer (102);
 importing collected learning measurements since the beginning till the last period (103) upon expiration of said refresh timer;
 applying an MLPDL (104) technique to predict breakpoints of the plurality of cellular towers one cellular tower at a time, wherein the breakpoint of a cell tower reflects the average number of users connected to said cell tower associated with the preferred maximum PRB utilization percentage of said cellular tower;
 applying the optimization inputs (105), i.e., imported topology information and predicted PRB utilization congestion thresholds;
 choosing the optimization algorithm (106);
 if BCDSA algorithm is chosen, performing BCDSA algorithm (107) to redistribute traffic as the result of changing power and handover thresholds of the plurality of cells to effectively redistribute traffic from a congested cells to noncongested cells thereby optimally reducing the congestion of the cellular network;
 if GA algorithm is chosen, performing GA algorithm (108) to redistribute traffic as the result of changing power and handover thresholds of the plurality of cells to effectively redistribute traffic from a congested cells to noncongested cells thereby optimally reducing the congestion of the cellular network;
 collecting the operating parameters of cellular towers from either BCDSA or GA algorithm (109); and
 going back to step (102) to wait again for the expiration of said refresh timer.
Any feature or combination of features described herein are included within the scope of the present invention provided that the features included in any such combination are not mutually inconsistent as will be apparent from the context, this specification, and the knowledge of one of ordinary skill in the art. Additional advantages and aspects of the present invention are apparent in the following detailed description and claims.
BRIEF DESCRIPTION OF THE ALGORITHMSAlgorithm 2 contains an algorithmic description of BCDSA algorithm.
Algorithm 2 contains an algorithmic description of GA algorithm.
This invention focuses on systematically finding power and handover settings of a cluster of LTE cells minimizing overall cluster congestion. First, a deep learning scheme predicts the PRB utilization congestion threshold of the plurality of cellular towers belonging to said cluster. Next, an optimization problem aiming at minimizing the congestion of said cluster is formulated using per cellular tower power and handover parameters as decision variables. The problem is then solved using two optimization techniques, namely, GA and BCDSA. Accordingly, an integrated set of method, program, and system aiming at minimizing the congestion of the cluster subject to load preservation and quality constraints are introduced. In an embodiment of the presented modeling and optimization of congestion algorithms, a 4G LTE cellular network cluster illustrated in
In some embodiments, the present invention presents a solution to congestion minimization by first predicting the PRB utilization congestion threshold of each cell tower as a function of connected User Equipments (UEs) thereby avoiding degradation of neighboring cells offered quality as the result of offloading users from congested cells. Utilizing the predicted PRB utilization congestion thresholds as operational constraints, optimal configurations of parameters _{i }and _{i }with i ε {1, . . . , N} that maximize traffic offloading are identified for the plurality of cells within a cluster set. Said configuration parameters satisfy minimum quality thresholds of the plurality of cells and preserve cluster loading. Low complexity of the solutions allow them to be embedded into live systems making real time decisions about traffic offloading. Hence, offered solutions can operate as intelligent Self Optimizing Network (iS ON) systems. Table 1 provides a listing of notations used in this paper.
LearningBased Breakpoint Modeling
First, the approach to learning PRB utilization congestion threshold of each LTE cell i in a cluster of cellular towers is discussed. Denoted by Λ_{i}, the average number of UEs connected to cell i associated with the congestion threshold of PRB utilization is predicted.
PRB under different loading levels of average connected users. For example, it is observed that cell LBQ06135B21 has a high PRB utilization at a low average connected UEs. On the other hand, cell LBQ04836B11 has a much lower PRB utilization for similar loading values of average connected UEs. Hence, cell LBQ04836B11 reaches 80% congestion threshold of PRB utilization at a much higher number of average connected UEs around 153 users, while cell LBQ06135B21 reaches the same threshold at around 74 UEs. It is evident that cell LBQ04836B11 is able to carry a larger number of UEs than cell LBQ06135B21 before reaching congestion threshold of PRB utilization. The question of interest is then how to predict the value of Λ_{i}, i.e., the average number of connected UEs crossing the PRB utilization congestion threshold for each cell i based on its unique characteristics.
MultiLayer Perceptron Deep Learning
In an embodiment, MLPDL is used to predict congestion threshold of individual LTE cells in a cluster of cell towers. The latter is equivalent to identifying the value of Λ_{i }for each cell i, i.e., the average number of connected UEs crossing the PRB utilization congestion threshold. The major challenge in learning is the identification of proper inputs leading to accurately predicted results. In what follows, associated details are discussed. In an embodiment, the fixed, fully connected, feedforward perceptron learning structure utilized for the task of LTE PRB utilization congestion threshold modeling consists of an input layer with nineteen processing elements to accept nineteen LTE input counters. In order to strike the balance between accuracy and complexity, the structure considers two to four hidden layers, each layer containing ten to twenty processing elements. The structure has an output layer with one processing element predicting the value of Λ_{i }for cell i.
In each iteration of learning, all inputs associated with a sample input are propagated in the forward direction from the input through hidden layers to generate an output. The output value is compared to the measured output and an output error is calculated. The output error is then propagated in the reverse direction to the input layer in order to adjust weighting functions between every pair of processing elements in adjacent layers. The process is repeated until reaching an acceptable threshold of output error. For evaluating the error, Root Mean Square Error (RMSE) is calculated between the measured PRB utilization congestion threshold from the collected data and MLPDL prediction.
Input Counters to Learning
One of the critical factors in generating accurately predicted results is the choice of input parameters, i.e., LTE counters. The goal is to utilize a group of available LTE counters that are most closely related to PRB utilization of cells. In a number of embodiments, various counters collected from the real network of a major US mobile operator over one week are investigated. Among the set of input data, some of these counter are average and peak connected UEs, PRB utilization, QCI, modulation scheme used, average and peak throughputs of UEs as well as cells, uplink SINR, CQI, spectral efficiency, average Receive reference Signal on Reference Power (RSRP), and Reference Signal Received Quality (RSRQ). In the first embodiment, average active UEs, average connected UEs, and peak connected UEs of a single cell are used to predict PRB utilization congestion threshold of that cell subsequently introducing an RMSE of 34%. Adding call attempts, average and peak number of ERABs, and total VoLTE calls results in an an RMSE of about 36%. In the next embodiment, adding traffic measures of VoLTE in Erlangs and data volume in Megabytes improves RMSE to 22%. It is important to note that this phase adds the actual voice and data loading of connected UEs on individual cells. The following phase adds QCI as presented in
Congestion Minimization
In additional embodiments, predicted PRB utilization congestion thresholds are utilized in an optimization problem aiming to reduce the overall congestion of a cluster of cellular towers by means of shifting traffic from congested cells to their noncongested neighboring cells. Shifting LTE traffic can be done in two ways. First, adjusting LTE cell power _{i }of a cell i results in shrinking the footprint of the cell hence shifting UEs on the border to the neighboring cells. Second, artificially changing the handover threshold _{j }of a neighboring LTE cell j results in making it look stronger thereby triggering an earlier handover. The latter effectively shrinks the footprint of cell i and shifts border UEs from cell i to cell j. However, traffic offloading has to be controlled to assure the volume of shifted traffic to a neighboring cell keeps the overall load of that neighboring cell below its threshold of congestion.
Hence, the problem aims at identifying the optimal settings of the operating parameters of each cell power _{i }and handover threshold _{i }in order to minimize the congestion of the cluster of cell towers as the result of shifting traffic from congested cells to their non congested neighbors. This is achieved subject to satisfying two constraints associated with the minimum acceptable quality experienced by a UE connected to a cell tower and preservation of the overall load of the cluster of cell towers.
Problem Description
The embodiment of interest attempts at minimizing the cluster congestion by offloading UEs connected to cells experiencing more than 80% PRB utilization to noncongested neighboring cells without congesting them. While any choice of congestion threshold may be considered in different embodiments, a value of 80% utilization is the typical choice of mobile operators preventing various performance issues such as handover failures and call drops.
The approach calls for a) reducing _{i }power of a congested cell i in order to shrink its footprint and hence shifting traffic to its neighbors, and b) changing the handover threshold _{j }of a noncongested neighboring cell j in order to increase the footprint of cell j. Both changes result in shifting existing connected UEs on cell i edges to be served by its neighboring cells at a slightly lower quality than the quality experienced when connected to the original cell i. The quality experienced by a UE connected to cell i is typically represented by SINR denoted as q_{i}.
Problem Formulation
In an embodiment of the invention, the formulated optimization problem is expressed as shown below where [x]^{+}=max(x,0).
The formulation attempts at minimizing Λ_{T }the total cluster congestion by changing power _{i }and handover threshold _{i }on a cellbycell basis. The optimization cost function is subject to two constraints. First, the total number of UEs connected to all cells has to sum up to the total load of the cluster. This constraint in essence guarantees the preservation of load within the cluster. Second, the quality experienced by a UE connected to cell i denoted by q_{i }has to meet a minimum acceptable quality threshold of Q explained shortly. The total traffic congestion Λ_{r }in Eq. (1) is the difference of the summation of three terms and predicted congestion threshold associated with all individual cells. These terms for cell i are the current UEs connected to cell i, the change in connected UEs associated with changing power , and the sum of changes in connected UEs associated with offloading users from cell i to neighboring cells j after changing handover threshold values of cell j,. Finally, Λ_{i }represents the predicted congestion threshold of cell i.
In the embodiment above, the optimization problem represents a nonlinear programming problem with a total of 2N decision variables _{i }and _{i }where i ε {1, . . . , N} and decision variables assume values from discrete sets. Next, a mathematical analysis defining individual terms of the optimization problem is provided.
The change in connected UEs associated with represents traffic offload to the neighboring cells as the result of shrinking the footprint of cell i after changing _{i}. Accordingly, is expressed by Eq. (4).
In the equation above, K_{2 }is a constant with typical values of −40, −30, and −20 dB/decade for urban, suburban, and rural environments, respectively. It has to be noted that Eq. (4) is derived utilizing Hata propagation model [8, 9] and assuming the traffic is homogeneously distributed in the serving area as depicted in [10,11].
Similarly, is expressed as a function of the traffic offload of cell i to its neighbor j and the area overlap percentage η_{i,j }between cells i and j.
While the overlap percentage can be calculated from handover statistics on a cell pair basis, η_{i,j }is set separately for front facing and cosite neighbors. To understand the definitions of front facing and cosite neighbors, note that in
Next, quality constraints are discussed. The average quality q_{i }of cell i after applying new settings is presented as shown below.
The impact to quality is mainly associated with the shift of cell boundaries due to Δ_{i}, Δ_{j}, or the sum of them combined. The combined effect results in shifting users at the edge of cell i to a neighboring cell j where they are served by a weaker signal and with a degraded quality. This shift is calculated for each serving cell i and each of its neighbors j. The worst quality value q_{i,j }is chosen to present the quality of cell i guaranteed not to be not than a minimum allowed quality level of Q.
In order to express q_{i,j }as a function of Δ_{i }and Δ_{j}, γ_{i }representing the SINR of a UE connected to cell i is chosen as the quality metric [8, 12]. When reducing the serving cell i power _{i}, the boundary of cell i shrinks forcing the UEs at r_{A′ }to be served at a lower quality by a neighboring cell. In environments of interest to this invention, the UEs at the boundary of the serving cell typically experience a reduction of q_{i }equivalent to the reduction in power _{i }and handover threshold _{1}. Hence, the variations in quality of a UE shifted from cell i to a neighboring cell j is expressed as shown below.
λγ_{i,j}=Δ+Δ_{j} (7)
Consequently, the quality impact is captured as shown below.
q_{i,j}=γ_{i,j}−Δγ_{i,j} (8)
In a typical embodiment of interest to this invention, UEs at a cell boundary experience a reference SINR value of zero dB. Further, a minimum SINR value of −3 dB is needed in order to support a minimum modulation scheme of QPSK for covered UEs [8, 13]. Therefore, Q is set to −3 dB.
Solution Approach
Considering the fact that the formulated problem is a nonlinear optimization problem in which decision variables assume discrete values, two algorithmic embodiments of namely BCDSA and GA are presented to solve the problem after adding a set of penalty terms _{i }and δ_{i }to the objective function [1416]. Penalty terms are added in order to enforce quality constraints. The penaltyaugmented objective function is then defined below.
In Eq. (9),
It has to be noted that δ_{i }is a weighted penalty factor applying a constant large hard penalty, set to 10^{6 }in one embodiment, for violating the load preservation constraint in equation (2) of cell i. Further, _{i }is a weighted penalty factor applying a constant large hard penalty, set to 10^{6 }in one embodiment, for violating the quality constraint in equation (3). Numerically, the load preservation constraint in equation (2) is met by balancing the offloading of connected UEs from a congested cell to its neighbors.
Block Coordinated Descent Simulated Annealing (BCDSA)
Inspired by the block coordinated descent optimization techniques [1719], the first algorithmic embodiment modifies the standard Simulated Annealing (SA) algorithm in an attempt to address the tradeoff between accuracy and complexity. Referred to as BCDSA algorithm, this algorithmic variation applies the SA algorithm to a partitioned set of decision variables, i.e., optimizing one set while keeping the other set fixed, then optimizing the other set while keeping the first set fixed, and alternating between the two sets. Alternating between two sets of decision variables occurs if the cost function does not change after few iterations of one set measured by a freeze factor ξ. There are two per cell decision variables, namely, Δ_{i }and Δ_{i}. Accordingly, the partitioning strategy splits the decision variables to two sets, namely the set of Δ_{i }and the set of Δ_{i }values. The BCDSA algorithm is explained in Algorithm 2.
The worst case time complexity of the BCDSA algorithm is in the order of O(σρN) considering its nested while loops. The number of iterations in the outer loop is set to
where T_{i}, T_{f}, and a are the initial temperature, final temperature, and cooling factor of BCDSA algorithm. following the number of temperature points from geometric distribution. The number of iterations in the inner loop is set to ρN where ρ is a fixed integer multiplier and N is the number of cellular towers.
With respect to convergence, BCDSA algorithm is conjectured to converge to a local optimal point in the vicinity of the global optimal solution of the formulated optimization problem. To support the claim, it is noted that [22] proves the convergence of SA algorithm to a local optimal point in the vicinity of the global optimal point for proper choices of parameters. Further, BCD algorithms are known to converge to stationary points if the Lagrangian function formed by the objective and the nonlinear constraint functions is convex or under milder conditions quasiconvex and hemivariate [2325]. The BCDSA algorithm is primarily an SA algorithm augmented by BCD techniques and hence the choices of parameters warrant its convergence to a local optimal point. The effect of BCD augmentation is in essence improving its average speed and robustness of convergence. In the absence of a mathematical proof, BCDSA is consistently observed to robustly converge to a vicinity of the global optimal solution, identified by exhaustive search, in higher speeds and high confidence intervals.
The worst case time complexity of the BCDSA algorithm is in the order of O(σρN) which is identical to that of standard SA. However, BCDSA has a better average time complexity compared to other SA alternatives. Further, it has much better success rates in converging to the vicinity of global optimal solutions than other SA alternatives.
Genetic Algorithm (GA)
The second algorithmic embodiment of this invention, GA, is driven from the natural evolution of creatures, with the survival of the fittest, and creates child generations that are usually better than parents. This algorithm depends heavily on randomness allowing it to explore vast solution spaces. GA is be able to identify global or nearglobal optimal points without getting trapped in local optima.
The GA algorithm goes through the following steps [21]:

 Generate an initial population of chromosomes denoted as the first generation.
 Each chromosome is comprised of a number of genes equal to the number of optimization parameters.
 Each gene is assigned a random value in a preset range.
 All chromosomes are evaluated and ranked using a fitness or cost function.
 The next generation of chromosomes is created using genetic operators including Selection, Crossover, and Mutation.
 New generations are evaluated and ranked in turn leading to the creation of yet other new generations.
 This process is repeated until a certain number of generations is created or until there is no improvement in the cost function for newer generations.
This process is summarized in
One of the commonly used GA operators is Selection. Applying Selection operator results in choosing a certain percentage of top ranked chromosomes with the highest utility values as parents of the next generation. In an embodiment, a top rank percentage of 2% is used. Another operator, Crossover, is used to combine two chromosomes to create a new chromosome. This is done under the assumption that combining higher fitness chromosomes could result in even better fitting chromosomes thereby improving the overall fitness of a generation. In Crossover, a pair of chromosomes are selected to create offsprings. As illustrated by
Algorithm 2 describes how the GA algorithm is applied to solve the optimization problem of interest to this invention.
The worst case time complexity of the GA algorithm is in the order of O(nN) where n is the GA initial population count, is a fixed real number multiplier depending on the number of decision variables and their ranges, and N is the number of cellular towers.
EXPERIMENTAL RESULTS Experimental SettingsIn evaluating the performance of the algorithms of this invention, a sample embodiment of LTE cellular towers depicted by
The embodiment represents a typical cluster of cellular towers used in a dense urban downtown of a US city. The cluster of embodiment has ten sites, with each site having three sectors or cells, each presented with an arrow. In this embodiment, arrows colored in red represent congested cells while those in black represent noncongested cells. As shown by the figure, only a number of but not all cells are congested and further congested cells have at least a neighbor that is not congested. In addition, the cellular network is operating in an urban environment with a propagation loss coefficient of K_{2}32−40 dB/decade. Furthermore, a handover margin of 40% is assumed from a cell to its two facing neighbors and 10% to its cosite neighbors.
Additionally, a reduction in _{i }or increase in _{j }results in a similar reduction in SINR for border users based on the selected urban environment and the typical inter site distance. Traffic is homogeneously distributed in the serving area and hence reduction in traffic served is at a rate similar to reduction in serving area. The range of variations of both Δ_{i }and Δ_{i }is [0, 3]dB with a granularity of 0.1 dB. Border users are assumed to be served with an SINR value of approximately 0 dB and a minimum acceptable value no smaller than −3 dB [8]. The latter is the minimum value of SINR needed to achieve QPSK coding and throughput as presented in
Last but not least, measurements have shown deep learning prediction RMSE errors in the range of [0.5%, 1%] for the congestion threshold of Λ_{i }of cell i associated with 80% PRB utilization. In consideration of the error, a safety margin of 1% is applied to the predicted value of Λ_{i }when running optimization. This ensures that noncongested cells accepting offloaded traffic do not exceed their congestion threshold associated with 80% PRB utilization as a result of error in predicting their breakpoints.
In evaluating performance, each GA experiment is run 10 times for each value of initial population count starting from 10 and ending at 200 chromosomes. Further, BCDSA algorithm is run 100 times. The purpose of running multiple iterations of each algorithm is to measure the best and average congestion reduction values and also to measure the consistency of algorithms in finding good solutions. A solution is considered good if the value of total carried traffic is within 1% of the best solution obtained using that algorithm and others for this problem.
Algorithmic Comparison Results
In comparing the results obtained from both algorithms, different aspects of performance are viewed in terms of i) cost measured as the algorithmic runtime, ii) improvement measured as best and average congestion reduction values, and iii) success rate measured as the percentage of good solutions, i.e., the number of solutions within 1% of the best solution. This last parameter also measures the consistency of an algorithm in finding good solutions.
In an attempt to improve optimization results, reduce convergence time, and improve success rate, GA is run with few initial population values. Scenarios of interest include the followings in which a) all and are initialized with a value of 0, b) all and are initialized with values of 1, c) and are initialized with values of 0 and 1 respectively, d) and are initialized with values of 0 and 2 respectively, e) and are initialized with values of 0 and 3 respectively, f) and are assigned random values.
Comparisons of average runtimes and success rates for various GA configurations is presented in
As seen by the results and while accommodating the offered load of 2836 connected UEs, the total volume of congested traffic, i.e., the number of UEs connected to cells with over 80% PRB utilization is reduced from 506 to 302 representing 40.3% overall congestion reduction within the cluster.
In observing the performance of the GA algorithm, significantly higher runtimes are observed compared to BCDSA algorithm. Optimal solutions usually result in _{i }variations in the range of 1 to 3 dB and _{i }variations close to zero. It is also observed that initializing the population with random values of and usually results in longer convergence times and lower total traffic volumes.
The difference in performance can be intuitively explained based on the understanding of how each algorithm works. On one hand, the GA algorithms creates multiple solutions in the population and attempts at optimizing them using crossover and mutations to reach a global optimum. Hence, the chance of getting to that global optimum is higher since it approaches the solution from various directions. This leads to a higher success rate. However, it takes longer to process all these solutions. On the other hand, BCDSA only attempts at navigating its way to the global optimum. Hence, it offers a much lower processing time than that of GA. However, there is a higher chance of getting trapped in a local minimum and missing the global minimum since BCDSA approaches the global minimum from only one direction. A good analogy to this would be hiring 100 amateur hikers to find the mountain summit, versus hiring one professional hiker to navigate around the terrain and find that summit.
Alterations, Modifications, and ClarificationsMany alterations and modifications may be made by those having ordinary skill in the art without departing from the spirit and scope of the invention. Therefore, it must be understood that the illustrated embodiment has been set forth only for the purposes of example and that it should not be taken as limiting the invention as defined by the following invention and its various embodiments.
Therefore, it must be understood that the illustrated embodiment has been set forth only for the purposes of example and that it should not be taken as limiting the invention as defined by the following claims. For example, notwithstanding the fact that the elements of a claim are set forth below in a certain combination, it must be expressly understood that the invention includes other combinations of fewer, more or different elements, which are disclosed in above even when not initially claimed in such combinations. A teaching that two elements are combined in a claimed combination is further to be understood as also allowing for a claimed combination in which the two elements are not combined with each other, but may be used alone or combined in other combinations. The excision of any disclosed element of the invention is explicitly contemplated as within the scope of the invention.
The words used in this specification to describe the invention and its various embodiments are to be understood not only in the sense of their commonly defined meanings, but to include by special definition in this specification structure, material or acts beyond the scope of the commonly defined meanings. Thus, if an element can be understood in the context of this specification as including more than one meaning, then its use in a claim must be understood as being generic to all possible meanings supported by the specification and by the word itself.
The definitions of the words or elements of the following claims are, therefore, defined in this specification to include not only the combination of elements which are literally set forth, but all equivalent structure, material or acts for performing substantially the same function in substantially the same way to obtain substantially the same result. In this sense it is therefore contemplated that an equivalent substitution of two or more elements may be made for any one of the elements in the claims below or that a single element may be substituted for two or more elements in a claim. Although elements may be described above as acting in certain combinations and even initially claimed as such, it is to be expressly understood that one or more elements from a claimed combination can in some cases be excised from the combination and that the claimed combination may be directed to a subcombination or variation of a subcombination.
Insubstantial changes from the claimed subject matter as viewed by a person with ordinary skill in the art, now known or later devised, are expressly contemplated as being equivalently within the scope of the claims. Therefore, obvious substitutions now or later known to one with ordinary skill in the art are defined to be within the scope of the defined elements.
The claims are thus to be understood to include what is specifically illustrated and described above, what is conceptionally equivalent, what can be obviously substituted and also what essentially incorporates the essential idea of the invention.
In some embodiments described herein using the phrase “comprising” includes embodiments that could be described as “consisting of”, and as such the written description requirement for claiming one or more embodiments of the present invention using the phrase “consisting of” is met.
Reference numbers cited in the claims are exemplary, for ease of review by the patent office only, and are not limiting in any way.
Figures are representatives of concepts only and the claims are not limited by the figures in any ways.
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Claims
1. A method of redistributing traffic from congested cellular towers to noncongested cellular towers in a 4G LTE cellular network for reducing congestion of said cellular network FIG. 17 wherein said cellular network comprises clusters, clusters comprise sites, and sites comprise cellular towers, and wherein the method comprises:
 a. importing per cellular tower information (101) including neighbor handover, traffic demand, traffic carried, average transmit power, and minimum acceptable quality;
 b. waiting for the expiration of a refresh timer (102);
 c. importing collected learning measurements since the beginning till the last period (103) upon expiration of said refresh timer;
 d. applying an MLPDL (104) technique to predict breakpoints of the plurality of cellular towers one cellular tower at a time, wherein the breakpoint of a cell tower reflects the average number of users connected to said cell tower associated with the preferred maximum PRB utilization percentage of said cellular tower;
 e. applying the optimization inputs (105), i.e., imported topology information and predicted PRB utilization congestion thresholds;
 f. choosing the optimization algorithm (106);
 g. if BCDSA algorithm is chosen, performing BCDSA algorithm (107) to redistribute traffic as the result of changing power and handover thresholds of the plurality of cells to effectively redistribute traffic from a congested cells to noncongested cells thereby optimally reducing the congestion of the cellular network;
 h. if GA algorithm is chosen, performing GA algorithm (108) to redistribute traffic as the result of changing power and handover thresholds of the plurality of cells to effectively redistribute traffic from a congested cells to noncongested cells thereby optimally reducing the congestion of the cellular network;
 i. collecting the operating parameters of cellular towers from either BCDSA or GA algorithm (109); and
 j. going back to step (102) to wait again for the expiration of said refresh timer.
2. The method of claim 1, wherein MLPDL technique utilizes a fixed structure fully connected perceptron network for predicting the plurality of the breakpoints of each cellular tower one cellular tower at a time.
3. The method of claim 2, wherein the fixed structure comprises an input layer, one or more hidden layers, and an output layer, and wherein each layer comprises a number of processing elements.
4. The method of claim 3, wherein data flow through each processing element comprises generating the output of processing element after applying a nonlinear function to individually weighted inputs of said processing element.
5. The method of claim 3, wherein inputs of a processing element comprise the outputs of all processing elements in the adjacent layer below the layer in which the processing element is located.
6. The method of claim 3, wherein the set of inputs to the processing elements of the input layer comprise collected historical data of the plurality of cellular towers within the cellular network.
7. The method of claim 2, wherein MLPDL technique provides an iterative learning process to improve the accuracy of the predicted breakpoint of each cellular tower individually calculated as the error between the actual value of the breakpoint and the output of MLPDL.
8. The method of claim 7, wherein the stoppage criterion of iterative learning process comprises reaching a maximum number of iterations or an error below a small threshold of accuracy.
9. The method of claim 7, wherein each learning iteration is comprised of a forward propagation of the input followed by a backward propagation of the output error.
10. The method of claim 9, wherein during forward propagation of each iteration inputs are propagated from the input layer toward the output layer through hidden layers one layer at a time to set all input and output states of all processing elements.
11. The method of claim 9, wherein during back propagation of each iteration the output error is propagated back toward the input layer through hidden layers one layer at a time to adjust the weighting function between each processing element and individual processing elements in the layer below.
12. The method of claim 1, wherein either BCDSA or GA algorithm applies changes to power and handover threshold of individual cellular towers as decision variables to reduce congestion.
13. The method of claim 12, wherein reducing the power of a cellular tower results in reducing the coverage boundary of said cellular tower hence shifting users connected to said cellular tower far from its center to neighboring cellular towers thereby reducing the overall congestion of said cellular tower.
14. The method of claim 12, wherein increasing the handover threshold of a cellular tower results in increasing the handover boundary of said cellular tower and shifting users from congested neighboring cellular towers to said cellular tower thereby reducing the congestion of congested neighboring cellular towers.
15. The method of claim 12, wherein the BCDSA algorithm provides a nested iterative process, in which the inner iterative process stops after reaching a maximum number of iterations and the outer iterative process stops after an initial temperature reaches a final temperature as the result of getting sequentially multiplied by a cooling factor with a value smaller than one.
16. The method of claim 15, wherein the BCDSA algorithm partitions the decision variables to two sets comprising a set of power variables and a set of handover threshold variables and optimizes one set of decision variables in each iteration of the inner iterative process while keeping the other set fixed at that iteration.
17. The method of claim 16, wherein the BCDSA algorithm changes the congestion of a cellular network in each iteration of the inner iterative process, comprising the steps of:
 a. choosing a random cell i;
 b. if optimizing power, subtracting a random value selected from within a range of predefined values from the current power value of cell i;
 c. else if optimizing handover threshold, adding a random value selected from within a range of predefined values to the current handover threshold value of cell i;
 d. calculating the change in the total congestion of said cellular network as the result of applying power or handover threshold change;
 e. accepting the new solution, if the change is negative;
 f. performing the following test, if the change is positive; i. generating a random number R in the range [0,1]; ii. accepting the new solution, if the exponential value of the negative ratio of the change and the current temperature is more than R; or iii. rejecting the new solution, otherwise.
18. The method of claim 17, wherein the BCDSA algorithm alternates between the set of power and the set of handover threshold decision variables within the inner iterative process based on comparing the previous and current values of the total congestion of the cellular network against freezing thresholds thereby reflecting minor improvements.
19. The method of claim 18, wherein freezing thresholds are set dynamically aiming at maximizing step improvement and minimizing runtime.
20. A computer program product stored in a computer readable nonvolatile and volatile storage medium for redistributing traffic from congested cellular towers to noncongested cellular towers in a 4G LTE cellular network to reduce congestion of said cellular network FIG. 17 wherein said cellular network comprises clusters, clusters comprise sites, and sites comprise cellular towers, and wherein the computer program comprises:
 a. code for importing per cellular tower information (101)) including neighbor handover, traffic demand, traffic carried, average transmit power, and minimum acceptable quality;
 b. code waiting for the expiration of a refresh timer (102);
 c. code for importing collected learning measurements since the beginning till the last period (103) upon expiration of said refresh timer;
 d. code for applying an MLPDL (104) technique to predict breakpoints of the plurality of cellular towers one cellular tower at a time, wherein the breakpoint of a cell tower reflects the average number of users connected to said cell tower associated with the preferred maximum PRB utilization percentage of said cellular tower;
 e. code for applying the optimization inputs (105), i.e., imported topology information and predicted PRB utilization congestion thresholds;
 f. code for choosing the optimization algorithm (106);
 g. if BCDSA algorithm is chosen, code for performing BCDSA algorithm (107) to redistribute traffic as the result of changing power and handover thresholds of the plurality of cells to effectively redistribute traffic from a congested cells to noncongested cells thereby optimally reducing the congestion of the cellular network;
 h. if GA algorithm is chosen, code for performing GA algorithm (108) to redistribute traffic as the result of changing power and handover thresholds of the plurality of cells to effectively redistribute traffic from a congested cells to noncongested cells thereby optimally reducing the congestion of the cellular network;
 i. code for collecting the operating parameters of cellular towers from either BCDSA or GA algorithm (109); and
 j. code for going back to step (102) to wait again for the expiration of said refresh timer.
21. The computer program of claim 20, wherein MLPDL technique utilizes a fixed structure fully connected perceptron network for predicting the plurality of the breakpoints of each cellular tower one cellular tower at a time.
22. The computer program of claim 21, wherein the fixed structure comprises an input layer, one or more hidden layers, and an output layer, and wherein each layer comprises a number of processing elements.
23. The computer program of claim 22, wherein data flow through each processing element comprises generating the output of processing element after applying a nonlinear function to individually weighted inputs of said processing element.
24. The computer program of claim 22, wherein inputs of a processing element comprise the outputs of all processing elements in the adjacent layer below the layer in which the processing element is located.
25. The computer program of claim 22, wherein the set of inputs to the processing elements of the input layer comprise collected historical data of the plurality of cellular towers within the cellular network.
26. The computer program of claim 21, wherein MLPDL technique provides an iterative learning process to improve the accuracy of the predicted breakpoint of each cellular tower individually calculated as the error between the actual value of the breakpoint and the output of MLPDL.
27. The computer program of claim 26, wherein the stoppage criterion of iterative learning process comprises reaching a maximum number of iterations or an error below a small threshold of accuracy.
28. The computer program of claim 26, wherein each learning iteration is comprised of a forward propagation of the input followed by a backward propagation of the output error.
29. The computer program of claim 28, wherein during forward propagation of each iteration inputs are propagated from the input layer toward the output layer through hidden layers one layer at a time to set all input and output states of all processing elements.
30. The computer program of claim 28, wherein during back propagation of each iteration the output error is propagated back toward the input layer through hidden layers one layer at a time to adjust the weighting function between each processing element and individual processing elements in the layer below.
31. The computer program of claim 20, wherein either BCDSA or GA algorithm applies changes to power and handover threshold of individual cellular towers as decision variables to reduce congestion.
32. The computer program of claim 31, wherein reducing the power of a cellular tower results in reducing the coverage boundary of said cellular tower hence shifting users connected to said cellular tower far from its center to neighboring cellular towers thereby reducing the overall congestion of said cellular tower.
33. The computer program of claim 31, wherein increasing the CIO of a cellular tower results in increasing the handover boundary of said cellular tower and shifting users from congested neighboring cellular towers to said cellular tower thereby reducing the congestion of congested neighboring cellular towers.
34. The computer program of claim 31, wherein the BCDSA algorithm provides a nested iterative process, in which the inner iterative process stops after reaching a maximum number of iterations and the outer iterative process stops after an initial temperature reaches a final temperature as the result of getting sequentially multiplied by a cooling factor with a value smaller than one.
35. The computer program of claim 34, wherein the BCDSA algorithm partitions the decision variables to two sets comprising a set of power variables and a set of handover threshold variables and optimizes one set of decision variables in each iteration of the inner iterative process while keeping the other set fixed at that iteration.
36. The computer program of claim 35, wherein the BCDSA algorithm changes the congestion of a cellular network in each iteration of the inner iterative process, comprising the steps of:
 a. choosing a random cell i;
 b. if optimizing power, subtracting a random value selected from within a range of predefined values from the current power value of cell i;
 c. else if optimizing handover threshold, adding a random value selected from within a range of predefined values to the current handover threshold value of cell i;
 d. calculating the change in the total congestion of said cellular network as the result of applying power or handover threshold change;
 e. accepting the new solution, if the change is negative;
 f. performing the following test, if the change is positive; i. generating a random number R in the range [0,1]; ii. accepting the new solution, if the exponential value of the negative ratio of the change and the current temperature is more than R; or iii. rejecting the new solution, otherwise.
37. The computer program of claim 36, wherein the BCDSA algorithm alternates between the set of handover threshold and the set of handover threshold decision variables within the inner iterative process based on comparing the previous and current values of the total congestion of the cellular network against freezing thresholds thereby reflecting minor improvements.
38. The computer program of claim 37, wherein freezing thresholds are set dynamically aiming at maximizing step improvement and minimizing runtime.
39. A system comprising processors and memory coupled to processors, the memory storing instructions readable by a computing device that, when executed by processors, cause processors to perform operations to redistribute traffic from congested cellular towers to noncongested cellular towers in a 4G LTE cellular network thereby reducing congestion of said cellular network FIG. 17 wherein said cellular network comprises clusters, clusters comprise sites, and sites comprise cellular towers, and wherein said operations comprise:
 a. means for importing per cellular tower information (101)) including neighbor handover, traffic demand, traffic carried, average transmit power, and minimum acceptable quality;
 b. means to wait for the expiration of a refresh timer (102);
 c. means for importing collected learning measurements since the beginning till the last period (103) upon expiration of said refresh timer;
 d. means for applying an MLPDL (104) technique to predict breakpoints of the plurality of cellular towers one cellular tower at a time, wherein the breakpoint of a cell tower reflects the average number of users connected to said cell tower associated with the preferred maximum PRB utilization percentage of said cellular tower;
 e. means for applying the optimization inputs (105), i.e., imported topology information and predicted PRB utilization congestion thresholds;
 f. choosing the optimization algorithm (106);
 g. if BCDSA algorithm is chosen, means for performing BCDSA algorithm (107) to redistribute traffic as the result of changing power and handover thresholds of the plurality of cells to effectively redistribute traffic from a congested cells to noncongested cells thereby optimally reducing the congestion of the cellular network;
 h. if GA algorithm is chosen, means for performing GA algorithm (108) to redistribute traffic as the result of changing power and handover thresholds of the plurality of cells to effectively redistribute traffic from a congested cells to noncongested cells thereby optimally reducing the congestion of the cellular network;
 i. means for collecting the operating parameters of cellular towers from either BCDSA or GA algorithm (109); and
 j. means for going back to step (102) to wait again for the expiration of said refresh timer.
40. The system of claim 39, wherein MLPDL technique utilizes a fixed structure fully connected perceptron network for predicting the plurality of the breakpoints of each cellular tower one cellular tower at a time.
41. The system of claim 40, wherein the fixed structure comprises an input layer, one or more hidden layers, and an output layer, and wherein each layer comprises a number of processing elements.
42. The system of claim 41, wherein data flow through each processing element comprises generating the output of processing element after applying a nonlinear function to individually weighted inputs of said processing element.
43. The system of claim 41, wherein inputs of a processing element comprise the outputs of all processing elements in the adjacent layer below the layer in which the processing element is located.
44. The system of claim 41, wherein the set of inputs to the processing elements of the input layer comprise collected historical data of the plurality of cellular towers within the cellular network.
45. The system of claim 40, wherein MLPDL technique provides an iterative learning process to improve the accuracy of the predicted breakpoint of each cellular tower individually calculated as the error between the actual value of the breakpoint and the output of MLPDL.
46. The system of claim 45, wherein the stoppage criterion of iterative learning process comprises reaching a maximum number of iterations or an error below a small threshold of accuracy.
47. The system of claim 45, wherein each learning iteration is comprised of a forward propagation of the input followed by a backward propagation of the output error.
48. The system of claim 47, wherein during forward propagation of each iteration inputs are propagated from the input layer toward the output layer through hidden layers one layer at a time to set all input and output states of all processing elements.
49. The system of claim 47, wherein during back propagation of each iteration the output error is propagated back toward the input layer through hidden layers one layer at a time to adjust the weighting function between each processing element and individual processing elements in the layer below.
50. The system of claim 39, wherein either BCDSA or GA algorithm applies changes to power power and handover threshold handover threshold of individual cellular towers as decision variables to reduce congestion.
51. The system of claim 50, wherein reducing the power of a cellular tower results in reducing the coverage boundary of said cellular tower hence shifting users connected to said cellular tower far from its center to neighboring cellular towers thereby reducing the overall congestion of said cellular tower.
52. The system of claim 50, wherein increasing the handover threshold of a cellular tower results in increasing the handover boundary of said cellular tower and shifting users from congested neighboring cellular towers to said cellular tower thereby reducing the congestion of congested neighboring cellular towers.
53. The system of claim 50, wherein the BCDSA algorithm provides a nested iterative process, in which the inner iterative process stops after reaching a maximum number of iterations and the outer iterative process stops after an initial temperature reaches a final temperature as the result of getting sequentially multiplied by a cooling factor with a value smaller than one.
54. The system of claim 53, wherein the BCDSA algorithm partitions the decision variables to two sets comprising a set of power variables and a set of handover threshold variables and optimizes one set of decision variables in each iteration of the inner iterative process while keeping the other set fixed at that iteration.
55. The system of claim 54, wherein the BCDSA algorithm changes the congestion of a cellular network in each iteration of the inner iterative process, comprising the steps of:
 a. choosing a random cell i;
 b. if optimizing power, subtracting a random value selected from within a range of predefined values from the current power value of cell i;
 c. else if optimizing handover threshold, adding a random value selected from within a range of predefined values to the current handover threshold value of cell i;
 d. calculating the change in the total congestion of said cellular network as the result of applying power or handover threshold change;
 e. accepting the new solution, if the change is negative;
 f. performing the following test, if the change is positive; i. generating a random number R in the range [0,1]; ii. accepting the new solution, if the exponential value of the negative ratio of the change and the current temperature is more than R; or iii. rejecting the new solution, otherwise.
56. The system of claim 55, wherein the BCDSA algorithm alternates between the set of power and the set of handover threshold decision variables within the inner iterative process based on comparing the previous and current values of the total congestion of the cellular network against freezing thresholds thereby reflecting minor improvements.
57. The system of claim 56, wherein freezing thresholds are set dynamically aiming at maximizing step improvement and minimizing runtime.
Type: Application
Filed: May 11, 2017
Publication Date: Dec 14, 2017
Patent Grant number: 10362520
Inventors: Homayoun Yousefi'zadeh (Irvine, CA), Amr Albanna (Irvine, CA)
Application Number: 15/593,109